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B样条函数 1

切比雪夫多项式 1

勒让德多项式 1

厄米多项式 1

失效概率 1

形状参数 1

彩色图像灰度化；子空间建模；二阶多项式模型；梯度相关相似；离散搜索 1

拉盖尔多项式 1

指数多项式样条函数 1

求根 1

结构可靠性 1

距离模糊；误差距离；多目标；对称多项式辅助的中国余数定理 1

高斯积分 1

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Inverse Kinematics Analysis of General 6R Serial Robot Mechanism Based on Groebner Base

WANG Yan, HANG Lu-bin, YANG Ting-li

《机械工程前沿（英文）》 2006年 第1卷 第1期   页码 115-124 doi: 10.1007/s11465-005-0022-7

摘要：

This study presents a solution for the inverse kinematics problem in serial 6R manipulator. Using only seven equations composed of Duffy s four kinematical equations containing three angles and three corresponding angles identical equations instead of the traditional 14 equations, the authors reduced the inverse kinematics problem in the general 6R manipulator to a univariate polynomial with a minimum degree based on the Groebner Base method. From that, they concluded that the maximum number of the solutions is 16, generally. Also, the mathematics mechanization method can be extended to solve other mechanism problems involving nonlinear equations symbolically.

关键词： identical     manipulator     univariate polynomial     mechanism     traditional    

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指数多项式均匀样条模型

赵颜利,平萍,刘凤玉

《中国工程科学》 2008年 第10卷 第7期   页码 147-152

摘要：

给出了k（ k ≥ ３） 阶指数多项式的均匀样条模型。该类模型具有很多与B 样条模型相同的性质，并 且增加了一个可调节的形状参数。由该模型构造的曲线，通过改变形状参数的取值，可以调整曲线接近其控 制多边形的程度。应用于CAD/CAM领域，可作为几何造型的一种新的有效模型。

关键词： 指数多项式样条函数     B样条函数     形状参数    

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高阶高斯积分节点的高精度数值计算

张庆礼,王晓梅,殷绍唐,江海河

《中国工程科学》 2008年 第10卷 第2期   页码 35-40

摘要：

在工程数值计算、X射线衍射线形分析、光谱学等领域常使用高斯数值积分，高斯积分的节点及权重因子是数值积分的必须数据。研究了高次勒让德、拉盖尔和厄米多项式的零 点，即高斯-勒让德、高斯-拉盖尔、高斯-厄米积分的节点的计算方法，给出了一种有效的高精度数值算法——搜索迭代方法（scan-iteration method，SIM）。根据勒让德、拉盖尔、厄米多项式的特点，对拉盖尔多项式、厄米多项式的定义稍做变化后，获得了计算多项 式值的稳定递推关系。求它们的根时，先在一定范围内以一定的步长搜索根所在的

关键词： 高斯积分     勒让德多项式     拉盖尔多项式     厄米多项式     求根    

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Enhancement of the polynomial functions response surface model for real-time analyzing ozone sensitivity

Jiangbo Jin, Yun Zhu, Jicheng Jang, Shuxiao Wang, Jia Xing, Pen-Chi Chiang, Shaojia Fan, Shicheng Long

《环境科学与工程前沿（英文）》 2021年 第15卷 第2期 doi: 10.1007/s11783-020-1323-0

摘要： Abstract • The calculation process and algorithm of response surface model (RSM) were enhanced. • The prediction errors of RSM in the margin and transition areas were greatly reduced. • The enhanced RSM was able to analyze O3-NOx-VOC sensitivity in real-time. • The O3 formations were mainly sensitive to VOC, for the two case study regions. Quantification of the nonlinearities between ambient ozone (O3) and the emissions of nitrogen oxides (NOx) and volatile organic compound (VOC) is a prerequisite for an effective O3 control strategy. An Enhanced polynomial functions Response Surface Model (Epf-RSM) with the capability to analyze O3-NOx-VOC sensitivities in real time was developed by integrating the hill-climbing adaptive method into the optimized Extended Response Surface Model (ERSM) system. The Epf-RSM could single out the best suited polynomial function for each grid cell to quantify the responses of O3 concentrations to precursor emission changes. Several comparisons between Epf-RSM and pf-ERSM (polynomial functions based ERSM) were performed using out-of-sample validation, together with comparisons of the spatial distribution and the Empirical Kinetic Modeling Approach diagrams. The comparison results showed that Epf-RSM effectively addressed the drawbacks of pf-ERSM with respect to over-fitting in the margin areas and high biases in the transition areas. The O3 concentrations predicted by Epf-RSM agreed well with Community Multi-scale Air Quality simulation results. The case study results in the Pearl River Delta and the north-western area of the Shandong province indicated that the O3 formations in the central areas of both the regions were more sensitive to anthropogenic VOC in January, April, and October, while more NOx-sensitive in July.

关键词： Response surface model     Hill-climbing algorithm     Ozone pollution     Precursor emissions     Control strategy    

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A new type of quadratic acceleration method

Changqing LI, Menglin LOU,

《结构与土木工程前沿（英文）》 2010年 第4卷 第3期   页码 302-310 doi: 10.1007/s11709-010-0026-1

摘要： The polynomial acceleration method for time history analysis is presented, in which accelerations between several equal neighboring time steps were assumed to be a polynomial function of time interval. With a higher order polynomial used, a higher accuracy can be obtained, but the stability field of the method becomes narrower. When stability field and computational accuracy are taken into account at the same time, the quadratic acceleration method is superior to linear and cubic acceleration methods in choosing the maximum acceptable time step size. It is also shown that the quadratic acceleration method has desirable arithmetic damp, amplitude decay rate and period elongation rate, though its conditional stability restricts its application in stiff structures.

关键词： polynomial acceleration method     convergence     stability     square acceleration method    

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A solution to stochastic unit commitment problem for a wind-thermal system coordination

B. SARAVANAN,Shreya MISHRA,Debrupa NAG

《能源前沿（英文）》 2014年 第8卷 第2期   页码 192-200 doi: 10.1007/s11708-014-0306-x

摘要： Unit commitment (UC) problem is one of the most important decision making problems in power system. In this paper the UC problem is solved by considering it as a real time problem by adding stochasticity in the generation side because of wind-thermal co-ordination system as well as stochasticity in the load side by incorporating the randomness of the load. The most important issue that needs to be addressed is the achievement of an economic unit commitment solution after solving UC as a real time problem. This paper proposes a hybrid approach to solve the stochastic unit commitment problem considering the volatile nature of wind and formulating the UC problem as a chance constrained problem in which the load is met with high probability over the entire time period.

关键词： unit commitment (UC)     randomness     wind generation     univariate     chance constrained    

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基于对称多项式辅助的中国余数定理的脉冲多普勒雷达多目标距离估计算法 Research Articles

曹成虎1,赵永波1,2

《信息与电子工程前沿（英文）》 2022年 第23卷 第2期   页码 304-316 doi: 10.1631/FITEE.2000418

摘要： 工作在高脉冲重复频率的脉冲多普勒雷达能避免多普勒模糊，但是高脉冲重复频率在许多场合导致距离模糊。目前，解决距离模糊的有效方案是基于波形设计，但是增加了雷达系统的复杂性。由于目标距离和量测距离的对应关系未知，传统的基于多脉冲重复频率方案，特别是中国余数定理，很难应用于多目标距离解模糊。本文旨在研究量测距离含有误差的基于中国余数定理多目标距离估计方法。提出基于对称多项式辅助的中国余数定理，能有效从含有误差的量测距离中重建多目标距离。封闭式鲁棒中国余数定理和基于Aitken加速算法的多项式方程求解方法能有效降低所提算法的计算复杂度。

关键词： 距离模糊；误差距离；多目标；对称多项式辅助的中国余数定理    

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Multiobjective trajectory optimization of intelligent electro-hydraulic shovel

《机械工程前沿（英文）》 2022年 第17卷 第4期 doi: 10.1007/s11465-022-0706-2

摘要： Multiobjective trajectory planning is still face challenges due to certain practical requirements and multiple contradicting objectives optimized simultaneously. In this paper, a multiobjective trajectory optimization approach that sets energy consumption, execution time, and excavation volume as the objective functions is presented for the electro-hydraulic shovel (EHS). The proposed cubic polynomial S-curve is employed to plan the crowd and hoist speed of EHS. Then, a novel hybrid constrained multiobjective evolutionary algorithm based on decomposition is proposed to deal with this constrained multiobjective optimization problem. The normalization of objectives is introduced to minimize the unfavorable effect of orders of magnitude. A novel hybrid constraint handling approach based on -constraint and the adaptive penalty function method is utilized to discover infeasible solution information and improve population diversity. Finally, the entropy weight technique for order preference by similarity to an ideal solution method is used to select the most satisfied solution from the Pareto optimal set. The performance of the proposed strategy is validated and analyzed by a series of simulation and experimental studies. Results show that the proposed approach can provide the high-quality Pareto optimal solutions and outperforms other trajectory optimization schemes investigated in this article.

关键词： trajectory planning     electro-hydraulic shovel     cubic polynomial S-curve     multiobjective optimization     entropy weight technique    

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Cusp points and assembly changing motions in the PRR-PR-PRR planar parallel manipulator

《机械工程前沿（英文）》 2023年 第18卷 第2期 doi: 10.1007/s11465-022-0743-x

摘要： Most parallel manipulators have multiple solutions to the direct kinematic problem. The ability to perform assembly changing motions has received the attention of a few researchers. Cusp points play an important role in the kinematic behavior. This study investigates the cusp points and assembly changing motions in a two degrees of freedom planar parallel manipulator. The direct kinematic problem of the manipulator yields a quartic polynomial equation. Each root in the equation determines the assembly configuration, and four solutions are obtained for a given set of actuated joint coordinates. By regarding the discriminant of the repeated roots of the quartic equation as an implicit function of two actuated joint coordinates, the direct kinematic singularity loci in the joint space are determined by the implicit function. Cusp points are then obtained by the intersection of a quadratic curve and a cubic curve. Two assembly changing motions by encircling different cusp points are highlighted, for each pair of solutions with the same sign of the determinants of the direct Jacobian matrices.

关键词： planar parallel manipulator     assembly changing motions     cusp points     quartic polynomial     discriminant of repeated roots    

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Robust topology optimization of multi-material lattice structures under material and load uncertainties

Yu-Chin CHAN, Kohei SHINTANI, Wei CHEN

《机械工程前沿（英文）》 2019年 第14卷 第2期   页码 141-152 doi: 10.1007/s11465-019-0531-4

摘要： Enabled by advancements in multi-material additive manufacturing, lightweight lattice structures consisting of networks of periodic unit cells have gained popularity due to their extraordinary performance and wide array of functions. This work proposes a density-based robust topology optimization method for meso- or macro-scale multi-material lattice structures under any combination of material and load uncertainties. The method utilizes a new generalized material interpolation scheme for an arbitrary number of materials, and employs univariate dimension reduction and Gauss-type quadrature to quantify and propagate uncertainty. By formulating the objective function as a weighted sum of the mean and standard deviation of compliance, the tradeoff between optimality and robustness can be studied and controlled. Examples of a cantilever beam lattice structure under various material and load uncertainty cases exhibit the efficiency and flexibility of the approach. The accuracy of univariate dimension reduction is validated by comparing the results to the Monte Carlo approach.

关键词： robust topology optimization     lattice structures     multi-material     material uncertainty     load uncertainty     univariate dimension reduction    

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Uncertainty propagation in dynamics of composite plates: A semi-analytical non-sampling-based approach

Mahdi FAKOOR, Hadi PARVIZ

《结构与土木工程前沿（英文）》 2020年 第14卷 第6期   页码 1359-1371 doi: 10.1007/s11709-020-0658-8

摘要： In this study, the influences of spatially varying stochastic properties on free vibration analysis of composite plates were investigated via development of a new approach named the deterministic-stochastic Galerkin-based semi-analytical method. The material properties including tensile modulus, shear modulus, and density of the plate were assumed to be spatially varying and uncertain. Gaussian fields with first-order Markov kernels were utilized to define the aforementioned material properties. The stochastic fields were decomposed via application of the Karhunen-Loeve theorem. A first-order shear deformation theory was assumed, following which the displacement field was defined using admissible trigonometric modes to derive the potential and kinetic energies. The stochastic equations of motion of the plate were obtained using the variational principle. The deterministic-stochastic Galerkin-based method was utilized to find the probability space of natural frequencies, and the corresponding mode shapes of the plate were determined using a polynomial chaos approach. The proposed method significantly reduced the size of the mathematical models of the structure, which is very useful for enhancing the computational efficiency of stochastic simulations. The methodology was verified using a stochastic finite element method and the available results in literature. The sensitivity of natural frequencies and corresponding mode shapes due to the uncertainty of material properties was investigated, and the results indicated that the higher-order modes are more sensitive to uncertainty propagation in spatially varying properties.

关键词： composite plate     spatially varying stochastic properties     Galerkin method     polynomial chaos approach     semi-analytical approach    

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Probabilistic stability of uncertain composite plates and stochastic irregularity in their buckling mode shapes: A semi-analytical non-intrusive approach

《结构与土木工程前沿（英文）》   页码 179-190 doi: 10.1007/s11709-022-0888-z

摘要： In this study, the mechanical properties of the composite plate were considered Gaussian random fields and their effects on the buckling load and corresponding mode shapes were studied by developing a semi-analytical non-intrusive approach. The random fields were decomposed by the Karhunen−Loève method. The strains were defined based on the assumptions of the first-order and higher-order shear-deformation theories. Stochastic equations of motion were extracted using Euler–Lagrange equations. The probabilistic response space was obtained by employing the non-intrusive polynomial chaos method. Finally, the effect of spatially varying stochastic properties on the critical load of the plate and the irregularity of buckling mode shapes and their sequences were studied for the first time. Our findings showed that different shear deformation plate theories could significantly influence the reliability of thicker plates under compressive loading. It is suggested that a linear relationship exists between the mechanical properties’ variation coefficient and critical loads’ variation coefficient. Also, in modeling the plate properties as random fields, a significant stochastic irregularity is obtained in buckling mode shapes, which is crucial in practical applications.

关键词： uncertain composite plate     stochastic assume mode method     Karhunen−Loève theorem     polynomial chaos approach     plate buckling     irregularity in buckling mode shapes    

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工程结构可靠性分析的高阶矩法研究

宫凤强,李夕兵,邓建

《中国工程科学》 2006年 第8卷 第5期   页码 69-73

摘要：

提出了工程结构可靠性分析的高阶矩方法。主要是基于数值逼近原理，以切比雪夫正交函数族{Tk(x)}做基，利用功能函数的高阶矩信息，通过计算功能函数概率密度函数的逼近表达式，然后根据工程结构可靠性的一般表达式来计算结构的失效概率，进行可靠性分析。通过经典分布函数的数值检验和结构构件失效概率的计算结果比较，表明了该方法在理论上的正确性和工程中的实用性。

关键词： 结构可靠性     高阶矩     切比雪夫多项式     失效概率    

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一种基于两步参数子空间模型的对比度保持彩色图像灰度化算法 Article

Hong-yang LU, Qie-gen LIU, Yu-hao WANG, Xiao-hua DENG

《信息与电子工程前沿（英文）》 2017年 第18卷 第11期   页码 1874-1882 doi: 10.1631/FITEE.1600017

摘要： rgb2gray转换模型是目前最为经典和流行的彩色图像灰度化方法。最新的研究表明，对一阶线性模型的三个加权参数进行自适应离散搜索具有良好的潜力。在本文中，我们提出一种两步法方式，将参数搜索策略扩充到二阶多变量多项式模型。该模型划分为三个子空间的和，本文论证了第一个子空间是最为重要的，并且第二个子空间可以看作为对其进行加细的部分。在模型的第一步，将梯度相似性测度（gradient correlation similarity, Gcs）用于第一个子空间，得到一个初步的灰度化图像。然后，再次使用Gcs对初步灰度图像和第二子空间所引出形成的候选图像进行最优解搜索。通过数值实验，在定量评价、定性视觉评价和算法复杂度方面表明了本方法的有效性。

关键词： 彩色图像灰度化；子空间建模；二阶多项式模型；梯度相关相似；离散搜索    

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Polynomial robust observer implementation based passive synchronization of nonlinear fractional-order

Alain Soup Tewa Kammogne, Michaux Noubé Kountchou, Romanic Kengne, Ahmad Taher Azar, Hilaire Bertrand Fotsin, Soup Teoua Michael Ouagni,kouaneteoua@yahoo.fr,aazar@psu.edu.sa,ahmad.azar@fci.bu.edu.eg

《信息与电子工程前沿（英文）》 2020年 第21卷 第9期   页码 1267-1412 doi: 10.1631/FITEE.1900430

摘要： A robust polynomial observer is designed based on passive synchronization of a given class of r Colpitts (FOC) systems with mismatched uncertainties and disturbances. The primary objective of the proposed observer is to minimize the effects of unknown bounded disturbances on the estimation of errors. A more practicable output-feedback passive controller is proposed using an adaptive polynomial state observer. The distributed approach of a continuous frequency of the FOC is considered to analyze the stability of the observer. Then we derive some stringent conditions for the robust passive synchronization using Finsler’s lemma based on the fractional Lyapunov stability theory. It is shown that the proposed method not only guarantees the asymptotic stability of the controller but also allows the derived adaptation law to remove the uncertainties within the nonlinear plant’s dynamics. The entire system using passivity is implemented with details in PSpice to demonstrate the feasibility of the proposed control scheme. The results of this research are illustrated using computer simulations for the control problem of the r chaotic Colpitts system. The proposed approach depicts an efficient and systematic control procedure for a large class of nonlinear systems with the fractional derivative.
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标题 作者 时间 类型 操作

Inverse Kinematics Analysis of General 6R Serial Robot Mechanism Based on Groebner Base

WANG Yan, HANG Lu-bin, YANG Ting-li

期刊论文

指数多项式均匀样条模型

赵颜利,平萍,刘凤玉

期刊论文

高阶高斯积分节点的高精度数值计算

张庆礼,王晓梅,殷绍唐,江海河

期刊论文

Enhancement of the polynomial functions response surface model for real-time analyzing ozone sensitivity

Jiangbo Jin, Yun Zhu, Jicheng Jang, Shuxiao Wang, Jia Xing, Pen-Chi Chiang, Shaojia Fan, Shicheng Long

期刊论文

A new type of quadratic acceleration method

Changqing LI, Menglin LOU,

期刊论文

A solution to stochastic unit commitment problem for a wind-thermal system coordination

B. SARAVANAN,Shreya MISHRA,Debrupa NAG

期刊论文

基于对称多项式辅助的中国余数定理的脉冲多普勒雷达多目标距离估计算法

曹成虎1,赵永波1,2

期刊论文

Multiobjective trajectory optimization of intelligent electro-hydraulic shovel

期刊论文

Cusp points and assembly changing motions in the PRR-PR-PRR planar parallel manipulator

期刊论文

Robust topology optimization of multi-material lattice structures under material and load uncertainties

Yu-Chin CHAN, Kohei SHINTANI, Wei CHEN

期刊论文

Uncertainty propagation in dynamics of composite plates: A semi-analytical non-sampling-based approach

Mahdi FAKOOR, Hadi PARVIZ

期刊论文

Probabilistic stability of uncertain composite plates and stochastic irregularity in their buckling mode shapes: A semi-analytical non-intrusive approach

期刊论文

工程结构可靠性分析的高阶矩法研究

宫凤强,李夕兵,邓建

期刊论文

一种基于两步参数子空间模型的对比度保持彩色图像灰度化算法

Hong-yang LU, Qie-gen LIU, Yu-hao WANG, Xiao-hua DENG

期刊论文

Polynomial robust observer implementation based passive synchronization of nonlinear fractional-order

Alain Soup Tewa Kammogne, Michaux Noubé Kountchou, Romanic Kengne, Ahmad Taher Azar, Hilaire Bertrand Fotsin, Soup Teoua Michael Ouagni,kouaneteoua@yahoo.fr,aazar@psu.edu.sa,ahmad.azar@fci.bu.edu.eg

期刊论文